Question

The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapor equal to \( p_v \). The saturation pressure of water at 300 K is \( p_{sat} \). The correct relation for the air-water mixture is

• A. \( p_v = 0.5 \, p_{sat} \)
• B. \( p_v = p_{sat} \)
• C. \( p_v = 0.622 \, p_{sat} \)
• D. \( p_v = 2 \, p_{sat} \)

Hint:

Relative humidity is the ratio of the actual water vapor pressure to the saturation pressure at a given temperature.

Answer 1

The Correct Option is A

The relative humidity \( RH \) is defined as the ratio of the partial pressure of water vapor (\( p_v \)) to the saturation pressure of water (\( p_{sat} \)) at the given temperature. We are given that the relative humidity is 50%, so: \[ RH = \frac{p_v}{p_{sat}} = 0.5 \] Thus, the partial pressure of water vapor is: \[ p_v = 0.5 \, p_{sat} \] Therefore, the correct answer is (A).